A328650 - OEIS

A328650

Triangular array read by rows: row n shows the coefficients of this polynomial of degree n: (1/n!)*(numerator of n-th derivative of 1)/(1-x-2x^2).

-1, 1, 4, -3, -6, -12, 5, 24, 24, 32, -11, -50, -120, -80, -80, 21, 132, 300, 480, 240, 192, -43, -294, -924, -1400, -1680, -672, -448, 85, 688, 2352, 4928, 5600, 5376, 1792, 1024, -171, -1530, -6192, -14112, -22176, -20160, -16128, -4608, -2304, 341, 3420

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

It appears that the number of nonconstant polynomial divisors of the n-th polynomial is given by A032741.

LINKS

Table of n, a(n) for n=0..46.

EXAMPLE

First eight rows:

-1;

1, 4;

3, -6, -12;

5, 24, 24, 32;

-11, -50, -120, -80, -80;

21, 132, 300, 480, 240, 192;

-43, -294, -924, -1400, -1680, -672, -448;

85, 688, 2352, 4928, 5600, 5376, 1792, 1024;

First eight polynomials:

-1

1 + 4 x

-3 (1 + 2 x + 4 x^2)

(1 + 4 x) (5 + 4 x + 8 x^2)

-11 - 50 x - 120 x^2 - 80 x^3 - 80 x^4

3 (1 + 4 x) (1 + 2 x + 4 x^2) (7 + 2 x + 4 x^2)

-43 - 294 x - 924 x^2 - 1400 x^3 - 1680 x^4 - 672 x^5 - 448 x^6

(1 + 4 x) (5 + 4 x + 8 x^2) (17 + 56 x + 120 x^2 + 32 x^3 + 32 x^4)

MATHEMATICA

g[x_, n_] := Numerator[ Factor[D[1/(1 - x - 2 x^2), {x, n}]]]

Column[Expand[Table[g[x, n]/n!, {n, 0, 12}]]] (* A328650 polynomials *)

h[n_] := CoefficientList[g[x, n]/n!, x];

Table[h[n], {n, 0, 10}] (* A328650 sequence *)

Column[%] (* A328650 array *)

CROSSREFS

Cf. A000032, A328646.

Sequence in context: A005522 A276202 A215336 * A343891 A232328 A276229

Adjacent sequences: A328647 A328648 A328649 * A328651 A328652 A328653

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Nov 01 2019

STATUS

approved